一个是副词，一个是形容词，所修饰的对象不同。a little ，词性为副词,修饰的形容词或者副词，中文意思是“有点，一些，一点”;a little of的词性是形容词，修饰的是名词。
一、a little，一点; 少许; 略微; 稍。
1、a little可作副词，常可以修饰动词、形容词副词原级和形容词副词比较级，表示各种程度。
I like English a little.
我有一点喜欢英语。(修饰动词)
Add a little of the warmed milk and allow to froth a little.
加一点温牛奶，并让它起点儿沫。(修饰动词)
The game slowed up a little in the second half.
比赛在下半场节奏略微放慢了一些。(修饰动词)
I could just eat a little something.
我只能吃一点点东西。(修饰动词)
He feels a little cold today.
今天他感到有点冷。(修饰形容词原级)
The discussion got a little heavy.
讨论变得有点严肃。(修饰形容词原级)
She's a little vague about her plans for next year.
她对她明年的计划不怎么明确。(修饰形容词原级)
Let's go somewhere a little less public.
咱们找一个僻静些的地方吧。(修饰形容词比较级)
You could try being a little more encouraging!
你可以试着多给人一些鼓励嘛！(修饰形容词比较级)
I should wait a little longer, if I were you.
假如我是你的话，我会再等一会儿。(修饰副词比较级)
He listens a little more carefully than I.他比我认真听一点。(修饰副词比较级)
2、a little可用来修饰不可数名词。
I have a little money in the bank to fall back on.
我在银行还有一点钱，需要时可以动用。
I go to the library for a little peace and quiet.
我到图书馆去清静一下。
There is a little food in the fridge, you needn’t buy any.
冰箱里有一些吃的，你不必买了。
With a little encouragement from his parents he should do well.
只要父母给点鼓励，他应该会干得很好。
二、a little of，一点, 少量。
a little of表示肯定意义，后面必须接不可数名词。
Add a little of the warmed milk and allow to froth a little.
加一点温牛奶，并让它起点儿沫。
She only drank a little of milk with her coffee.
她喝了点添加牛奶的咖啡里。
I need a little of time to finish this task.
我需要一点时间来完成这个任务。
He complained a little of a nagging pain between his shoulder blades
他有几句提到说肩胛骨之间一直在疼。
I find that a little of Jerry's company can go a long way.
我发觉跟杰里待上一会儿就受不了啦。
I've only read a little of the book so far.
这本书我才读了一小部分。
Could you please add a little of salt to the soup?
不能往汤里再加点盐?
She added a little of salt to the soup.
她加了一点盐到汤里。
He showed a little of interest in the project.
他对这个项目表现出了一点点兴趣。
I only need a little of sugar for the recipe.
我只需要点点糖来做这个菜谱。
The water is a little cold. Please give me a little of warn water.
这水有点冷。请给我一点热水。
There is a little of doubt in my mind about the validity of this research.
我对这个研究的可靠性还有一些怀疑。
There is only a little of sugar left in the jar.
罐子里只剩下一点点糖。
a little of也可以接形容词：
I'm feeling a little of tired today.
今天我感觉有点累。
The weather is a little of chilly.
天气有点冷。